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Elastodynamic response of three-dimensional icosahedral quasi-crystals under mechanical loadings is presented in this article. Two kinds of cases are considered here, in which the plane problem and anti-plane problem are included. The phonon and phason elastic fundamental fields along with their coupling effect in crack analysis are explicitly presented in terms of the theoretical and numerical analyses. Using the finite difference method, some numerical results of stresses, displacements, and normalized dynamic stress intensity factor are obtained. By comparing the results of quasi-crystals, this article reveals the influence of phonon and phason elastic fundamental fields, which occupy an important position in dynamic deformation behavior of quasi-crystals. Of course, phonon–phason coupling effect also should not be neglected.

Dynamic response of an icosahedral quasi-crystalline medium with a Griffith crack under mechanical loadings